Lock cylinders having an axial freewheel are known from the prior art. In the lock cylinders disclosed by the prior art, if an improper object is used in operative connection with a lock cylinder, the lock cylinder is decoupled from the bearing. During the decoupling, a cam portion of a coupling element makes its way into a groove present on the housing, so that a rotational movement of an output element configured as an espagnolette is prevented if, for instance, a tool engages the espagnolette in order to forcibly open a lock when the espagnolette is subsequently turned by the tool. In the prior art it is disadvantageous, however, that the groove in the housing, which groove is positively connected to the cam of the disengaging sleeve, for structural reasons adjoins a central center axis of the lock cylinder. The result of this is that, with the aid of the tool which engages the espagnolette, a low force action or applied moment is sufficient to release the positive connection between groove and cam. The resistance moment acting between groove and cam is then insufficient to combat the applied moment acting on the espagnolette, so that the espagnolette can be forcibly rotated in order to open a lock without a proper key.